1/2x+1/3y=-7/6;1/2x+4y=27/2

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x+3y=14

Solution for 1/2x+1/3y=-7/6;1/2x+4y=27/2 system of equations: 


  • /| (1/2)*x+(1/3)*y-(-7/6) = 0| (1/2)*x+4*y-(27/2) = 0
  • We try to solve the equation: (1/2)*x+(1/3)*y-(-7/6) = 0
  • 1/2*x+1/3*y+7/6 = 0 // - 1/2*x+7/6
  • 1/3*y = -(1/2*x+7/6) // : 1/3
  • y = (-(1/2*x+7/6))/1/3
  • y = -3*(1/2*x+7/6)
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| (1/2)*x-3*4*(1/2*x+7/6)-(27/2) = 0| y = -3*(1/2*x+7/6)
  • x/2-12*(1/2*x+7/6)-27/2 = 0
  • -11/2*x-14-27/2 = 0
  • -11/2*x-55/2 = 0
  • -11/2*x-55/2 = 0 // + 55/2
  • -11/2*x = 55/2 // : -11/2
  • x = 55/2/(-11/2)
  • x = -5
  • We insert the solution into one of the initial equations of our system of equations
  • For y = -3*(1/2*x+7/6): 
  • y = -3*(7/6-5*1/2)
  • y = -3*(7/6-5/2)
  • y = -3*(-4/3)
  • y = 4/3*3
  • y = 4
  • We get a system of equations:
  • /| y = 4| x = -5

 

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